Let (X,x) be an isolated complete intersection singularity of dimension \(n\geq 2\). The main result of this note is a formula for the difference of the Milnor number \(\mu\) (X,x) and dim \(T^ 1_{X,x}\) (the dimension of the base of a miniversal deformation of (X,x)). It is of the form: \(\mu(X,x)-\dim T^ 1_{X,x}=\sum^{n-1}_{p=0}h^{p,0}(X,x)+a_ 1+a_ 2+a_ 3,\) where \(h^{p,q}(X,x)\) denotes the (p,q)-Hodge number of the mixed Hodge structure which is naturally defined on the local cohomology group \(H^ n(X,X-\{x\})\) and the \(a_ i's\) are dimensions of vector spaces associated to (X,x). In particular, \(\mu(X,x)\geq \dim T^ 1_{X,x},\) which had been conjectured by \textit{G.-M. Greuel} [Math. Ann. 250, 157-173 (1980; Zbl 0417.14003)].